Multi angle

H 1 Criteria for equivalence between power series and polynomials

Auteurs : Kucharz, Wojciech (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Let $A$ be the ring of formal power series in $n$ variables over a field $K$ of characteristic zero. Two power series $f$ and $g$ in $A$ are said to be equivalent if there exists a $K$-automorphism of $A$ transforming $f$ into $g$. In my talk I will review criteria for a power series to be equivalent to a power series which is a polynomial in at least some of the variables. For example, each power series in $A$ is equivalent to a polynomial in two variables whose coefficients are power series in $n - 2$ variables. In particular, each power series in two variables over $K$ is equivalent to a polynomial with coefficients in $K$. Similar results are valid for convergent power series, assuming that the field $K$ is endowed with an absolute value and is complete. In the special case of convergent power series over the field of real numbers some weaker notions of equivalence will be also considered. I will report on works of several mathematicians giving simple proofs. Some open problems will be included.

    singularities - power series

    Codes MSC :
    14B05 - Singularities
    32B05 - Analytic algebras and generalizations, preparation theorems
    58C25 - Differentiable maps

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 17/02/15
      Date de captation : 05/02/15
      Collection : Algebraic and Complex Geometry
      Sous collection : Research talks
      Format : quicktime ; audio/x-aac
      Domaine : Algebraic & Complex Geometry
      Durée : 01:02:30
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-02-05_Kucharz.mp4

    Informations sur la rencontre

    Nom de la rencontre : Applications of Artin approximation in singularity theory / Applications de l'approximation de Artin en théorie des singularités
    Organisateurs de la rencontre : Hauser, Herwig ; Rond, Guillaume
    Dates : 02/02/15 - 06/02/15
    Année de la rencontre : 2015
    URL Congrès : https://conferences.cirm-math.fr/1474.html

    Citation Data

    DOI : 10.24350/CIRM.V.18693103
    Cite this video as: Kucharz, Wojciech (2015). Criteria for equivalence between power series and polynomials. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18693103
    URI : http://dx.doi.org/10.24350/CIRM.V.18693103


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